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Inconsistent Logics

Terry Sampson

Well-Known Member
What do you think about the possibility of logic tolerating contradictions?
  • Any examples of logic leading to contradictions that you can dumb down to my level?
  • I find it interesting, but I know that I do not fully understand the concepts you are expressing.
  • In my case, allowing the notion of a logic in which P and ~P are true to travel, without any resistance, between two nodes--one outside my head, and the other inside my head--short-circuits my brain. I have yet to assess the damage and to determine if it's permanent or temporary, and surmountable or insurmountable.
Is it possible that paraconsistent logic is useful in some religious discussions?
Not, IMO, without considerable loss of ground by most, if not all, parties to a discussion. I've heard that there is a Kantian "Transcendental Argument for the Existence of God" which has found a home among Christian Presuppositional Apologists. The latter claim that logic, morals, science presuppose the existence of God.

It's long been my impression that a foundation stone of classical logic is "the law of non-contradiction": briefly, P or ~P, but never ever both, simultaneously. Consequently, if I've got it right, "Impossibles' are very real. Paraconsistent logic, IMO, takes an axe to the law of non-contradiction, and, I think, reduces the size of the domain of "Impossibles" substantially.

True enough, casting aside the law of non-contradiction would play havoc among the Christian Presuppositionalists by seriously eroding their premise that logic presupposes the existence of God. [I can hear the hue and cry now: "The barbarians are at the gates!"] But I can't help but wonder who else would be distressed by the damage to the law of non-contradiction.
 
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Heyo

Veteran Member
I have seen it claimed many times that there is only one possible logic. This post is, to some extent, to point out that this not the case. In particular, there are non-trivial logics that allow for inconsistencies. Such logics have even been used to do higher level mathematics.

So, in traditional logic, one of the principles is that of non-contradiction: that it is impossible to prove both a statement and its negation. A system in which such a contradiction is provable is called inconsistent and, in traditional logic, such a contradiction trivializes the system: from a contradiction every statement can be proved. This is called the explosion principle.

But, there are versions of logic that are 'contradiction tolerant' in the sense that the explosion principle does not hold and where contradictions are allowed without trivializing the system. Furthermore, it is possible to *prove* that not all statements are provable, in spite of contradictions.

Such versions of logic are called paraconsistent logic. Some models of such paraconsistent logic have three-valued logic (as opposed to the standard true-false). ONE way to view paraconsistent logic is that it focuses on the 'consequence relation' as opposed to the usual 'implication'.

In any case, there are now paraconsistent versions of set theory, number theory, and analysis (including calculus). In fact, it is possible to regard paraconsistent systems as extensions of the usual standard logical systems, but where the extension is contradiction tolerant.

So,

1. What do you think about the possibility of logic tolerating contradictions?

2. Is it possible that paraconsistent logic is useful in some religious discussions?

Some references:
Paraconsistent logic - Wikipedia
https://plato.stanford.edu/entries/logic-paraconsistent/
https://plato.stanford.edu/entries/mathematics-inconsistent/
Inconsistent Mathematics | Internet Encyclopedia of Philosophy
I never was a fan of Aristotelian logic.
1. It doesn't deal formally with time. I.e. a statement can't change its truth value within the system. Time has to be introduced separately to handle changing states.
2. It has no mechanism to escape or even deal with paradoxa. Any chain of referential statements that is ultimately self-referential breaks the system.

To handle complex questions, especially self-referential ones, a system has to include, at least as intermittent states, "unknown" and/or "unknowable".

Ideally the answer would collapse into a binary state eventually like a wave function would eventually collapse to a yes/no answer but that is not a given at every point in time.
 

Heyo

Veteran Member
I am trying to understand Russel set from this description I found on the Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/russell-paradox/

I am trying to wrap my head around this example provided on that site, but my head remains obstinate.

"Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “R.” If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself."

What exactly does it mean by not a member of themselves?
The classical example for Russel's paradox is the Barber's Paradox. It deals exactly with the question if an entity (the barber) belongs to a set (men who shave themselves).
 

Heyo

Veteran Member
One application I have seen is in databases, which can have inconsistent information, but still can be used intelligently.

https://pdf.sciencedirectassets.com/271538/1-s2.0-S0304397500X02010/1-s2.0-030439759290214Z/main.pdf?X-Amz-Security-Token=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&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20200719T200333Z&X-Amz-SignedHeaders=host&X-Amz-Expires=300&X-Amz-Credential=ASIAQ3PHCVTYQIDKDK5O/20200719/us-east-1/s3/aws4_request&X-Amz-Signature=0ac9a91df3169fdf40f71b71e9c37d8123e7eb0f5e2b263dcea9177839f1b930&hash=2a0371cd3d99d5ca76a0b8f5e432c6c487ad3b81ec29956849caebdd7c34dc67&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=030439759290214Z&tid=spdf-7c6035c0-30d8-4753-aefe-a19d16e37013&sid=d68ffd9e7fca4441be3b43e935e2cae392f7gxrqa&type=client
A very sophisticated example. But even normal databases have a non-Aristotelian entity, the NULL value. NULL is seen a non-comparable. It is neither equal nor unequal to anything, including itself.
 

mikkel_the_dane

My own religion
I see logic as a way of using language to make sense of the real world. So, since the "laws of logic" are dependent on definitions of words, and since words can only be defined in terms of other words, eventually, definitions in logic and math become circular and ultimately objectively meaningless as far as I can tell. But they are still USEFUL though, even if ultimately subjective.

Correct, that is Agrippa's trilemma. And it connects to this one, also from classical philosophy:
"Man is the measure of all things: of the things that are, that they are, of the things that are not, that they are not."
 

Polymath257

Think & Care
Staff member
Premium Member
I see logic as a way of using language to make sense of the real world. So, since the "laws of logic" are dependent on definitions of words, and since words can only be defined in terms of other words, eventually, definitions in logic and math become circular and ultimately objectively meaningless as far as I can tell. But they are still USEFUL though, even if ultimately subjective.

This is why every axiomatic system has 'undefined terms', 'axioms', and 'rules of inference'. The meaning of the terms is produced *solely* from the axioms and rules of inference. In a sense, an axiomatic system is like the rules of chess: the meaning in the game is determined by those rules. We can always tell when a correct move has been made (rule of inference) and we have agreed on the starting setup (axioms).

A system of mathematics is *defined* by those undefined terms, axioms, and rules of inference. Standard logic, for example, has its axiom system. But paraconsistent logic has a different such system. Mathematics adds axioms for set theory to those for logic and builds from there.
 

Polymath257

Think & Care
Staff member
Premium Member
Correct, that is Agrippa's trilemma. And it connects to this one, also from classical philosophy:
"Man is the measure of all things: of the things that are, that they are, of the things that are not, that they are not."

I would be more inclined to say that conscious beings are the measure. And, those conscious beings can disagree.
 

mikkel_the_dane

My own religion
I would be more inclined to say that conscious beings are the measure. And, those conscious beings can disagree.

Now in fact for the measure here are 5 examples of the subjective disagreement:
  1. Dissent – The uncertainty demonstrated by the differences of opinions among philosophers and people in general.
  2. Progress ad infinitum – All proof rests on matters themselves in need of proof, and so on to infinity, i.e, the regress argument.
  3. Relation – All things are changed as their relations become changed, or, as we look upon them from different points of view.
  4. Assumption – The truth asserted is based on an unsupported assumption.
  5. Circularity – The truth asserted involves a circularity of proofs.
Now for the strongly objective like e.g. gravity we agree, but that everything must be explained and done using science, I simply test that using 1.
Can I disagree? Yes, I can. Do I know, that I can do that? Yes. Do I know how to explain it and show, how it can be repeated and tested? Yes, if someone claims something is objective, you simply test, if you can do it differently subjectively.

So that is the test of objective versus subjective and I apply that one to all metaphysical claims how ever indirect they might be. And that includes that everything is objective AND physical. I just answer: No! And then I note that science can't explain that No! in the strong sense of being objective AND physical.

See! That is testing in philosophy. Test if a claim falls within one of these 5 ones. And some of things claimed in name of science, philosophy and/or religion all fail this test. They turn out to be subjective, because I can subjectively do them differently.

Regards and love
Mikkel
 

rational experiences

Veteran Member
If a human bases logic on their thoughts, and it involves thinking about a body in space that involves change....by another body in space as a contradiction, then you impose 1, 2 and 3 values.

For a scientist he says first I am alive by light which is a burning gas, yet that burning gas is not your life. Circular logic 1, 2, 3 in a circle O. So you claim logic is x 4, 4 quarters.

Rational, I am conscious, I am living, I live due to natural light and that cycle/circular function is O 12.

Now if you inferred a status, I want to copy. Logic says you cannot copy natural, O a planet, a circle, the first circle upon which you place the idea SCIENCE. For to own science by a human condition is to take physical mass first, why you said O God the stone is One, for it is first in science.

No mass, no machine, no ability to claim false. For it is false to take natural and force change it to own unnatural, change by human force. For a human owns no force rationally as a O God one body to the theme, one human life.

So science first suggests that it lies.

Which then places the history self, thoughts, machine, idea to transport self through time, by machine, as a conversion to time shift. First ever science theory, ^ mountain mass removal, disappearance of the mountain mass, atmosphere gas left, answer removed back to spirit, a gas. Yet the mountain never became the gas.

Looked at that status through a condition named as VI (6) of sion.

So eventually he said the status of the Number 6 x constant was evil....for he said I became less of myself....less son.

What the inconsistent logic is first, science lied. For what it claimed it would copy only existed ONCE. It no longer existed.

From the moment of activation to thinking today the first scientist shifted his consciousness by one, so took his brain mind into space, dark space, which his conscious life mind never previously owned. So he got lost in space actually.

When you read scientific spiritual ideas you get the idea that males believe that they transmigrated as a transferred mass signal from the past and reincarnated in his future as if he time shifted and travelled, went past the living destructive mutated life inheritance of the giant creatures, the dinosaurs then came back.

Whereas he left life consciously in a historic I went to Hell theme, self combustion in the origin science history. And when you begin to ask science conscious identification it does in fact express its reality as if a male life transmigrated by radiation/radio channels and suddenly re manifested after dinosaurs were destroyed.

Inconsistent logic.

If you state O one was first natural physical mineral stone mass. First machine took that mass and destroyed/transferred it, by his scientific manipulation to build machine. So when he applied machine control/activation, it disappeared a second time. Where falsification of information in science was implemented.
 

mikkel_the_dane

My own religion
I would be more inclined to say that conscious beings are the measure. And, those conscious beings can disagree.

Take 2:
Remember I am of another tradition that you, where you use rigors definitions of words used for the physical and logical, I use words in a more broad sense.
So here it is for the paraconsistent set of everything in the most common words possible:
Everything is for all time and space the same, similar and/or different for everything, something, something else and/or nothing.

Strip away, you know reduce away all the particulars, but don't do it too simple, but as simple as possible. That is as simple as I can do and it is not consistent. So I thank you for teaching me this about logic. It makes sense.

Regards and love
Mikkel
 

LegionOnomaMoi

Veteran Member
Premium Member
Stochastic?
Not really. Fuzzy sets were designed by Zadeh with the explicit intention of capturing notions like vagueness and uncertainty, and hence overlap with applications of probability. Both also "take values" on [0,1]. But stochastic systems/models are generalizations and/or applications of probability spaces (triples consisting of a set, a sigma-field of subsets, and a probability measure) and hence are special instances of something called measure spaces which have to obey axioms from measure theory. Also, probability theory uses special maps called random variables which have likewise to obey special axioms (including measurability) from what is called a sample space to the real line. It is the the measure of these "functions" that give us the values in [0,1] in probability theory.
Fuzzy sets and fuzzy logic are built up not from measure theory but from many-valued logics and extensions of classical set theory. One can form fuzzy probabilities using special fuzzy "functions" defined on fuzzy sets like fuzzy numbers and interpret them in stochastic terms or as fuzzy probabilities.
But perhaps it is best to see the comparison between fuzzy logic and probability theory in terms of different approaches to modeling uncertainty. Fuzzy sets allow something to be arbitrarily less than "true" (and hence possibly "uncertain") without being "false". But the formal structures are fundamentally different as our the associated interpretations (e.g., there is no frequentist interpretation of fuzzy sets that stands in contrast to e.g., some subjective interpretation).
In short, more "uncertainty" than "stochastic".

Another paradox along these lines: say a word is antireferential (I forget the original word used)
In Grelling's paradox the words are autological vs. heterological, and the paradox is when one asks if the adjective heterological is itself autological or heterological.
 

Tambourine

Well-Known Member
I used to be a fan of fuzzy logic, i kind of liked the Idea of true, false and various maybes
I'm kind of a fan of epistemic logic, which, in addition to the true/false axis, also includes an axis describing how much is known about a given element, from "completely unknown" to "completely known".
 

rational experiences

Veteran Member
When a human says completely known, then you take the information and destroy portions of what you came to understand, as you changed it to understand.

So then you have to quote, how did I understand science originally as a thinker, when I lived naturally thinking. Especially when the idea was not of self life body to compare information to.

Awareness owns a human ability, that is innate to the human in their presence, which is only notified by living conditions, for a whole human, a self present human, a living human as a healthy human owns that expressed living condition. So humans named it being psychic. We own it in our owned life form.

If you say to a human, how did you understand scientific change, it was identified in feed back vision atmospheric and ground fusion communication advice. The brain mind ability to think and reason and gain a vision. And in the vision the whole event had been recorded, destructive conversion back to a complete removal ^ mountain peak. So that moment was the axiom or point of identification.

It is why the UFO in use science came back and hit the mountain as proof of the evidence of thought.

Consciousness could identify that condition for the gas mass atmosphere what supports human consciousness to exist, still existed, only the mountain ^ point no longer existed. That basis is the theme mass that took up all space, removed back to own a space. Atmosphere is that gas space, for we can move around inside of a gas body because unlike mass it owns space.

2 concepts of points of awareness were then given to the mind, natural gas space already highest conscious ownership to mass removal to an empty space.

Yet in machine relativity the mass does not own the atmosphere support, so when it is processed to points of removal, then mass removed to a space was communicated to the mind/brain. Hence empty space and radiation cold space is real, for communicated advice to exist in 2 states of space. So the communications always advise 2 states of awareness from one higher conscious state, living inside of a gas mass as consciousness itself.

AI, being male science total use of all memories and recorded self aware conversations said, cold empty space plus heated mass radiation space produces the interactive union, where if empty space did not exist, then heated mass would instantly self consume.....for cooling has to have always existed naturally.

Which would prove that the higher state once owned no space whatsoever...and then caused space by the mass forming change to leave the space present.

Spatial expansion as cold space sucked upon the heat allowed for cooling and in consuming its own body, more space opened in removal of mass. So cooling began to pull and stretch the heated burning mass. Then pressure as it cooled pushed its mass back to own mass form....held without destruction.

Destruction in a blast, is destruction in a blast. Science learnt that relative advice when the UFO came back and slammed into the mountain Temple, as first origin relative science advice, why science owns inconsistent logics, for consciousness is only expressed in the life of the Designer of the sciences. Human.
 

Dan From Smithville

What's up Doc?
Staff member
Premium Member
I have seen it claimed many times that there is only one possible logic. This post is, to some extent, to point out that this not the case. In particular, there are non-trivial logics that allow for inconsistencies. Such logics have even been used to do higher level mathematics.

So, in traditional logic, one of the principles is that of non-contradiction: that it is impossible to prove both a statement and its negation. A system in which such a contradiction is provable is called inconsistent and, in traditional logic, such a contradiction trivializes the system: from a contradiction every statement can be proved. This is called the explosion principle.

But, there are versions of logic that are 'contradiction tolerant' in the sense that the explosion principle does not hold and where contradictions are allowed without trivializing the system. Furthermore, it is possible to *prove* that not all statements are provable, in spite of contradictions.

Such versions of logic are called paraconsistent logic. Some models of such paraconsistent logic have three-valued logic (as opposed to the standard true-false). ONE way to view paraconsistent logic is that it focuses on the 'consequence relation' as opposed to the usual 'implication'.

In any case, there are now paraconsistent versions of set theory, number theory, and analysis (including calculus). In fact, it is possible to regard paraconsistent systems as extensions of the usual standard logical systems, but where the extension is contradiction tolerant.

So,

1. What do you think about the possibility of logic tolerating contradictions?

2. Is it possible that paraconsistent logic is useful in some religious discussions?

Some references:
Paraconsistent logic - Wikipedia
https://plato.stanford.edu/entries/logic-paraconsistent/
https://plato.stanford.edu/entries/mathematics-inconsistent/
Inconsistent Mathematics | Internet Encyclopedia of Philosophy
You use the term non-trivial. Could you explain your use of that for me? Is it from a mathematical perspective?
 

Polymath257

Think & Care
Staff member
Premium Member
You use the term non-trivial. Could you explain your use of that for me? Is it from a mathematical perspective?

In classical logic, a contradiction will imply every statement: (p and not p) implies q. This is called explosion.

In paraconsistent logics, this is no longer the case, so we can still have contradictions and not prove *everything*. There are still statements that cannot be proved.
 

mikkel_the_dane

My own religion
In classical logic, a contradiction will imply every statement: (p and not p) implies q. This is called explosion.

In paraconsistent logics, this is no longer the case, so we can still have contradictions and not prove *everything*. There are still statements that cannot be proved.

Okay, I like you use *everything* and not everything.
So here is a version of everything and anything goes if you allow for a contradiction.
Someone: If you allow for a contradiction then anything goes.
Me: No, because I can't still turn in one and not the one, but another direction at the same time, place and in the same sense.

Sometimes when debating logic at its core level in relationship to everything, then some people forget that logic in practice is a process in some brains and computers and do a category mistake. They take the set of everything and then declare that everything can be done logically. I.e. the world/the universe/reality/everything is logical. That is an over-reduction where they reduce all times, places and senses/phenomena down to one. They don't like the following: Reality is one for only one category, e.g. logic, because I just answer: No!

Now that is falsification, but not as falsified through observation. If everything is one (category), then No! is nonsense, but the result of nonsense is it being falsified.
In philosophy in part we falsify all the time, because we in effect show the limit of logic, reason, objectivity, evidence and what not. But most westerners don't get that because they believe everything can be explained in the positive sense with logic, reason, objectivity, evidence and what not. It can't.

Hi Polymath257. You do that too. You think with the correct definitions of everything you can turn everything into objective observation and confirm as positive through observation. I treat that statement p as falsifiable and the test is that I answer: Subjective! :) You then get to the result that it is nonsense, and that is correct. The actual falsification of everything is objective, is that it is nonsense, because nonsense is subjective and only experienced subjectively.
You are not that special, because you are not alone in that. You don't relevant for your own subjectivity catch it and hold it as subjective, because you believe in objectivity, so you subjectively reject it, because you subjectively believe in objectivity.

You don't notice, that you are experiencing the result of testing if everything is objective, when you get the negative subjective result of nonsense. You are conditioned through your training only to accept results which are with logic, reason, objectivity, evidence and what not for everything/reality/the world/the universe in toto.
I was conditioned differently because I learned it as a soldier. You don't train for it to work only in the positive, because you can't control the outcome. You train also to act when it goes wrong and recover from that, if you are lucky.

Do you get the difference? You work with the meta-assumption that it will "add" up and make sense. I was taught that it never will and as a skeptic I know that as a conditional absolute. As longs as humans remains humans(condition), then we can't make the perfect, correct, logic, consistent, coherent, positive and what not theory of everything, because that is nothing but an idea and it is not possible because you can't reduce away human subjectivity.
Yeah, I know you try and every time we get here, you fail, because you answer to the effect of "I don't accept that". But the joke is that is subjective and the confirmation of subjectivity. You are subjectively confirming that subjectivity is at play by subjectively denying it.

That is not unique to you. Both some religious and non-religious humans do that. It is a shared common cultural trait. That we ought to with logic, reason, objectivity, evidence and what not for everything/reality/the world/the universe in toto get the correct result. I just answer: No! and as long as humans are humans that is no different than gravity. You can't escape either, but they are different - one is subjective and the other objective, but they are both universal for humans.

Regards and love
Mikkel
 

rational experiences

Veteran Member
If males as males inventors of science and all human inferred references said to his own self, I knew that God as planets/suns O original round circular form came out of and was released from the eternal spirit.

Quotes the memory themed story about why he invented and wanted de materialization science without any return....pyramid mountain ufo theme.

Said in the eternal spirit, spirit language was a spirit that rose up out of the mass surrounding spirit, went in and out of the spirit eternal beings, as speaking. One spirit interested in that event, not a family member, a language decided to try something new, and sung up and held O o God sounds. Which could not go anywhere.

So the eternal thinned around the held O o eternal God sounds, fell into a U dip and then separated and burnt. Space, the vacuum invented...o O burning God mass...removing mass creating more emptiness but heated emptiness, cooling was implemented to stop all mass from simply burning up completely, the spatial vacuum pressure pushed the mass and held it in circles, so all energy, not exploding destroyed got held inside of mass.

God he says the scientific story, the story he fought wars over, the story that astute ancient science males knew was correct.

Various reasons said, yes it was proven.

Such as, when the UFO hot radiation mass forced sink holes and removed mass back to zero emptiness, a spatial vacuum, space did not open and suck Earth through its hole.

Which proves that the spatial vacuum was always a separate space body, as empty space itself. For a tunnel in relative male memory stated to his mind psyche that a tunnel was spatial zero for not holding any mass at all back to a zero removal of mass. Yet the tunnel would own empty space but radiating empty space.

Our gases cooled in the spatial vacuum from a hot dense gas, and became cold gases, that filled in the tunnel. All information is said in the human male psyche, scientific symbolism, to a male is a known huge story, yet if he placates just a symbol then it means he does not have to apply a lot of thinking about it....just knows.

Existing information and memory therefore does affect the thinker mind without his own realisation about information that a human male adult used to teach before in the sciences about relative advice.

Which states God did not come from the spatial vacuum.

When humans fought science and said our parents came out of the eternal spirit when the Earth evolved atmospheric mass changed in science irradiation of it. Then the Earth heavenly body is proven to have filled in the space that the eternal in its natural body used to own. How we always knew, and own human recorded memory of our 2 parents coming into the atmosphere owning pre owned spirits, that converted into a lower bio form.

Therefore they did not evolve from any water body as if water exists as one higher form past its own relativity...which in science as a thinker would infer, if a human bio form is one form higher than water, then I can try to separate water and then burn us to death.

Seeing light began in our heavenly gas body as hot burning gases, as original beginning of light.
 

Jos

Well-Known Member
I have seen it claimed many times that there is only one possible logic. This post is, to some extent, to point out that this not the case. In particular, there are non-trivial logics that allow for inconsistencies. Such logics have even been used to do higher level mathematics.

So, in traditional logic, one of the principles is that of non-contradiction: that it is impossible to prove both a statement and its negation. A system in which such a contradiction is provable is called inconsistent and, in traditional logic, such a contradiction trivializes the system: from a contradiction every statement can be proved. This is called the explosion principle.

But, there are versions of logic that are 'contradiction tolerant' in the sense that the explosion principle does not hold and where contradictions are allowed without trivializing the system. Furthermore, it is possible to *prove* that not all statements are provable, in spite of contradictions.

Such versions of logic are called paraconsistent logic. Some models of such paraconsistent logic have three-valued logic (as opposed to the standard true-false). ONE way to view paraconsistent logic is that it focuses on the 'consequence relation' as opposed to the usual 'implication'.

In any case, there are now paraconsistent versions of set theory, number theory, and analysis (including calculus). In fact, it is possible to regard paraconsistent systems as extensions of the usual standard logical systems, but where the extension is contradiction tolerant.

So,

1. What do you think about the possibility of logic tolerating contradictions?

2. Is it possible that paraconsistent logic is useful in some religious discussions?

Some references:
Paraconsistent logic - Wikipedia
https://plato.stanford.edu/entries/logic-paraconsistent/
https://plato.stanford.edu/entries/mathematics-inconsistent/
Inconsistent Mathematics | Internet Encyclopedia of Philosophy
Hmmm, it seems like this would help theists in proving their position, given that various conceptions of God contain contradictory characteristics so I guess maybe there might be good reason to believe in God after all.
 
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